Correct Answer - Option 5 :
x = y or relation between x and y can not be established.
Given:
I. x2 - 11x + 24 = 0
II. y2 - 13y + 40 = 0
Calculation:
From I,
I. x2 - 11x + 24 = 0
⇒ x2 - 8x - 3x + 24 = 0
⇒ x(x - 8) - 3(x - 8) = 0
⇒ (x - 8)(x - 3) = 0
Taking,
⇒ (x - 8) = 0 or (x - 3) = 0
⇒ x = 8 or 3
From II,
y2 - 13y + 40 = 0
⇒ y2 - 8y - 5y + 40 = 0
⇒ y(y - 8) - 5(y - 8) = 0
⇒ (y - 8)(y - 5) = 0
Taking,
⇒ (y - 8) = 0 or (y - 5) = 0
⇒ y = 8 or 5
Comparison between x and y (via Tabulation):
Value of x
|
Value of y
|
Relation
|
8
|
8
|
x = y
|
8
|
5
|
x > y
|
3
|
8
|
x < y
|
3
|
5
|
x < y
|
∴ x = y or relation between x and y can not be established.